The surface plasmon modes supported by a nondiffracting 90° bigrating consisting of three grooves per repeat period with one slightly shallower than the other two are characterized by studying the reflectivity from the structure as a function of the angle of incidence and the incident wavelength (11.3<λ0<16.7 mm). This structure supports two remarkably angle-independent modes plus a further, lower-energy mode which is more dispersive. Experimental reflectivity is compared with that calculated using a finite element model. In addition, to understand the character of each of the modes, the spatial form of the electromagnetic fields at the resonant frequencies are explored.